In this paper we introduce a novel methodology to transmit the origin to the center of a polygon in a molecule structure such that the special axis be perpendicular to the plane containing the polygon. The mathematical calculation are described completely and the algorithm will be showed as a computer program.

We devise dynamic algorithms for the following (weak) visibility polygon computation problems: • Maintaining visibility polygon of a fixed point located interior to simple polygon amid vertex insertions and deletions to simple polygon. • Answering visibility polygon query corresponding to any point located exterior to simple polygon amid vertex insertions and deletions to simple polygon. • Main...

In this work, we study a prism with a cross section in polygon rolling on a ramp inclined at a small angle. The prism under gravity rolls purely around each individual edge, intermittently interrupted by a sequence of face collisions between the side face of the prism and the ramp. By limiting the prism in a planar motion, we propose a mathematical model to deal with the events of the impacts. ...

Our aim is to prove a Poncelet type theorem for a line configuration on the complex projective plane P. More precisely, we say that a polygon with 2n sides joining 2n vertices A1, A2, · · · , A2n is well inscribed in a configuration Ln of n lines if each line of the configuration contains exactly two points among A1, A2, · · · , A2n. Then we prove : Theorem Let Ln be a configuration of n lines ...

Let $$C_{k_1}, \ldots , C_{k_n}$$ be cycles with $$k_i\ge 2$$ vertices ( $$1\le i\le n$$ ). By attaching these n together in a linear order, we obtain graph called polygon chain. cyclic graph, which is ring if it can embedded on the plane; and twisted Möbius band. It known that sandpile group of chain always cyclic. Furthermore, there exist edge generators. In this paper, not only show any (twi...

Visibility computation is a classical problem in computer graphics. A wide variety of algorithms provides solutions with a different accuracy. However, the four dimensional nature of the 3D visibility has prevented for a long time from leading to exact from-polygon visibility algorithms. Recently, the two first tractable solutions were presented by Nirenstein, then Bittner. Their works give the...